Problem: Multiply the following complex numbers: $({3}) \cdot ({-3-2i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({3}) \cdot ({-3-2i}) = $ $ ({3} \cdot {-3}) + ({3} \cdot {-2}i) + ({0}i \cdot {-3}) + ({0}i \cdot {-2}i) $ Then simplify the terms: $ (-9) + (-6i) + (0i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -9 + (-6 + 0)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -9 + (-6 + 0)i - 0 $ The result is simplified: $ (-9 - 0) + (-6i) = -9-6i $